Energy Sinks for Lee Waves in Shear Flow

Abstract

AbstractMicrostructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation ratesεon average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave actionE/ωL=E/|kU| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currentsU, where the intrinsic or Lagrangian frequencyωL= |kU| ↓ |f| andkthe along-stream horizontal wavenumber, wherekU≡k⋅V. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidthN/f. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes andN/fratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speedUand topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.